Hadamard Expansions and Hyperasymptotic Evaluation: an Extension of the Method of Steepest Descents
The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a deta...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2011
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 141 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (viii, 243 pages) |
| ISBN: | 9780511753626 |
| DOI: | 10.1017/CBO9780511753626 |
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| 505 | 8 | |a Preface; 1. Asymptotics of Laplace-type integrals; 2. Hadamard expansion of Laplace integrals; 3. Hadamard expansion of Laplace-type integrals; 4. Applications | |
| 520 | |a The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics | ||
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Datensatz im Suchindex
| _version_ | 1804176884232093696 |
|---|---|
| any_adam_object | |
| author | Paris, R. B. |
| author_facet | Paris, R. B. |
| author_role | aut |
| author_sort | Paris, R. B. |
| author_variant | r b p rb rbp |
| building | Verbundindex |
| bvnumber | BV043941924 |
| classification_rvk | SK 450 |
| collection | ZDB-20-CBO |
| contents | Preface; 1. Asymptotics of Laplace-type integrals; 2. Hadamard expansion of Laplace integrals; 3. Hadamard expansion of Laplace-type integrals; 4. Applications |
| ctrlnum | (ZDB-20-CBO)CR9780511753626 (OCoLC)907964362 (DE-599)BVBBV043941924 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.45 |
| dewey-search | 515/.45 |
| dewey-sort | 3515 245 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511753626 |
| format | Electronic eBook |
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| id | DE-604.BV043941924 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511753626 |
| language | English |
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| publisher | Cambridge University Press |
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| series2 | Encyclopedia of mathematics and its applications |
| spelling | Paris, R. B. Verfasser aut Hadamard Expansions and Hyperasymptotic Evaluation an Extension of the Method of Steepest Descents R.B. Paris Hadamard Expansions & Hyperasymptotic Evaluation Cambridge Cambridge University Press 2011 1 online resource (viii, 243 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 141 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Preface; 1. Asymptotics of Laplace-type integrals; 2. Hadamard expansion of Laplace integrals; 3. Hadamard expansion of Laplace-type integrals; 4. Applications The author describes the recently developed theory of Hadamard expansions applied to the high-precision (hyperasymptotic) evaluation of Laplace and Laplace-type integrals. This brand new method builds on the well-known asymptotic method of steepest descents, of which the opening chapter gives a detailed account illustrated by a series of examples of increasing complexity. A discussion of uniformity problems associated with various coalescence phenomena, the Stokes phenomenon and hyperasymptotics of Laplace-type integrals follows. The remaining chapters deal with the Hadamard expansion of Laplace integrals, with and without saddle points. Problems of different types of saddle coalescence are also discussed. The text is illustrated with many numerical examples, which help the reader to understand the level of accuracy achievable. The author also considers applications to some important special functions. This book is ideal for graduate students and researchers working in asymptotics Integral equations / Asymptotic theory Asymptotic expansions Asymptotische Entwicklung (DE-588)4112609-9 gnd rswk-swf Asymptotik (DE-588)4126634-1 gnd rswk-swf Laplace-Transformation (DE-588)4034577-4 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Integralgleichung (DE-588)4027229-1 gnd rswk-swf Laplace-Transformation (DE-588)4034577-4 s Asymptotische Entwicklung (DE-588)4112609-9 s Numerisches Verfahren (DE-588)4128130-5 s DE-604 Integralgleichung (DE-588)4027229-1 s Asymptotik (DE-588)4126634-1 s Erscheint auch als Druckausgabe 978-1-107-00258-6 https://doi.org/10.1017/CBO9780511753626 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Paris, R. B. Hadamard Expansions and Hyperasymptotic Evaluation an Extension of the Method of Steepest Descents Preface; 1. Asymptotics of Laplace-type integrals; 2. Hadamard expansion of Laplace integrals; 3. Hadamard expansion of Laplace-type integrals; 4. Applications Integral equations / Asymptotic theory Asymptotic expansions Asymptotische Entwicklung (DE-588)4112609-9 gnd Asymptotik (DE-588)4126634-1 gnd Laplace-Transformation (DE-588)4034577-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4112609-9 (DE-588)4126634-1 (DE-588)4034577-4 (DE-588)4128130-5 (DE-588)4027229-1 |
| title | Hadamard Expansions and Hyperasymptotic Evaluation an Extension of the Method of Steepest Descents |
| title_alt | Hadamard Expansions & Hyperasymptotic Evaluation |
| title_auth | Hadamard Expansions and Hyperasymptotic Evaluation an Extension of the Method of Steepest Descents |
| title_exact_search | Hadamard Expansions and Hyperasymptotic Evaluation an Extension of the Method of Steepest Descents |
| title_full | Hadamard Expansions and Hyperasymptotic Evaluation an Extension of the Method of Steepest Descents R.B. Paris |
| title_fullStr | Hadamard Expansions and Hyperasymptotic Evaluation an Extension of the Method of Steepest Descents R.B. Paris |
| title_full_unstemmed | Hadamard Expansions and Hyperasymptotic Evaluation an Extension of the Method of Steepest Descents R.B. Paris |
| title_short | Hadamard Expansions and Hyperasymptotic Evaluation |
| title_sort | hadamard expansions and hyperasymptotic evaluation an extension of the method of steepest descents |
| title_sub | an Extension of the Method of Steepest Descents |
| topic | Integral equations / Asymptotic theory Asymptotic expansions Asymptotische Entwicklung (DE-588)4112609-9 gnd Asymptotik (DE-588)4126634-1 gnd Laplace-Transformation (DE-588)4034577-4 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Integral equations / Asymptotic theory Asymptotic expansions Asymptotische Entwicklung Asymptotik Laplace-Transformation Numerisches Verfahren Integralgleichung |
| url | https://doi.org/10.1017/CBO9780511753626 |
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